A two-stroke internal combustion engine mounted on a handheld engine-driven working machine has a piston disposed in a cylinder and connected to a crankshaft, an ignition plug disposed in an upper portion of the cylinder, and an ignition control device activating the ignition plug. Effective activation of the ignition plug ignites fuel-air mixture in the cylinder to combust it, and inflation of the combusted air gives a force to the piston so as to move the piston from a top dead center position to a bottom dead center position. The ignition control device can set an ignition timing of the ignition plug with respect to the top dead center position of the piston (for example, a BTDC angle which is an angle of a crankshaft before the top dead center position).
The ignition control device is normally configured to set the ignition timing within a low speed range (for example, equal to or lower than 4,000 rpm) to a first BTDC angle A1 near the top dead center position of the piston and advance the ignition timing within a high speed range (for example, equal to or higher than 9,000 rpm) to a second BTDC angle A2 (see FIG. 13). This is because an output within the high speed range is enhanced. The ignition timing within a medium speed range (for example, 4,000-9,000 rpm) is defined so as to connect the ignition timing within the low speed range with the ignition timing within the high speed range (see, for example, Patent Publication 1).